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2016-05-01T06:04:59+05:30
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 \left \{ {{y=5x-8} \atop {x=6x+3}} \right.  

Arrange equation  variables for elimination :

 \left \{ {{y-5x=-8} \atop {x-6x=3}} \right.
   y -   6x = 3
-  y -  5x = -8
______________
-x =  11

For y :

y - 6 x = 3

y - 6 ( - 11 ) = 3

y + 66 = 3

y = 3 - 66

y = -63

x = - 11      y = -63
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2016-05-01T10:48:14+05:30
Let it be       y=5x-8 - ( equation 1 )
let it be       y=6x+3 - ( equation 2 )

by elimination process  { equation 2 - equation 1 }

 y = 5x-8 (-) y=6x+3
( here in the above subtraction we can directly cancel the y because " {y+(-y)} = 0 "
⇒  5x = 8 (-) 6x = 3  
∴ -x = 11

To know the value of x
⇒ y - 6x = 3
( we know the value of x so we will substitute it in the above step )
⇒ y- 6(-11) = 3
⇒ y+66 = 3
⇒ y = 3-66
∴ y = -63

The value of " x = -11 " and " y = -63 "
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